## Spectral Resolution and Slit Width

Below is a conservative estimate of the trend of resolution or FWHM (full-width at half-maximum) versus slit width for the instrument using a TEK CCD. The spatial scale is ~0.69 arcsecs/pixel. It should be pointed out that there is a general trend of slightly poorer focus as one goes from the center of the field to the edge. In the spatial direction, the trend is about a 20% degradation when going from center-to-edge along a spectral line (at field center).

## Slit Width Selection

The usual procedure for slit width selection has been to match the resolution of the detector by dividing the actual slit width by the so-called demagnification factor, or the ratio of collimator-to-camera focal lengths. However, for spectrographs such as the RC spectrograph, this approximation is not always valid. For cases when the collimator-to-camera angle is greater than ~15 degrees, the full expression for projected slit width should be used.

```		w = r (fcam / fcoll) W
```

Here w is the projected slit width, W the actual (physical) slit width, and r is the "grating anamorphic magnification". The factor r is a function of the grating tilt and collimator-camera angle, i.e.

```		r = cos(t + phi/2) / cos(t - phi/2)
```

where phi is the collimator-camera angle (46 degrees) and t is the grating tilt. For the UV Fast Camera, the camera-to-collimator focal ratio is ~0.23 . At large grating inclinations the anamorphic demagnification factor becomes significant. In these cases the slit can be opened slightly wider without degrading the resolution. See F. Schweizer's article PASP 91, No. 539, 149, 1979 for more information. For a complete table of grating tilts for the RC Spectrograph see the FTP version of the manual.

Be aware that at high grating inclinations (tilt <=3500) the camera becomes over-filled resulting in throughput loss. This is a problem only with higher dispersion gratings.

deveny@noao.edu
Friday, August 4, 1995